Finite Group Databasebeta

← #14424419

Subgroups — #14424419

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92098C211yesmaximal, characteristic, complemented
2C22×C3×C5×SD16C211yesmaximal, characteristic, complemented
3#11756564C211yesmaximal, characteristic, complemented
4C2×#91821C211yesmaximal, characteristic, complemented
5#11751326C211yesmaximal, characteristic, complemented
6#11751273C214yesmaximal, complemented
7#11751271C214yesmaximal, complemented
8#11751214C211yesmaximal, characteristic, complemented
9#11751211C211yesmaximal, characteristic, complemented
10#10615591—31nomaximal, Hall
11C22×C3×C5×Q8C2211yescharacteristic
12C22×C3×C5×D4C2211yescharacteristic
13#92098—24no—
14#92098—24no—
15C2×#6821—21no—
16C2×#6821C2212yescomplemented
17C2×Q8×D15—21no—
18C2×Q8×D15C2212yescomplemented
19C2×#6817—22no—
20C2×#6817C2211yescharacteristic
21C2×#6817C2211yescharacteristic
22C2×C3×C5×SD16—24no—
23C2×C3×C5×SD16C2214yes—
24C22×C3×C5×C8C2211yescharacteristic
25#91842—22no—
26#91829—21no—
27#91827C2214yes—
28#91825—21no—
29C2×#6716C2212yes—
30#91821—24no—
31C2×#6715C2212yes—
32#91815C2211yescharacteristic
33C2×#6710C2211yescharacteristic
34#91119C2214yescomplemented
35#91105C2212yescomplemented
36#91104C2214yescomplemented
37#91100C2212yescomplemented
38#83860—51nomaximal, Hall
39C2×#4147—31no—
40C22×C5×SD16D311yescharacteristic, complemented
41#66139—31no—
42C2×#4078—31no—
43#65514—31no—
44#65461—34no—
45#65459—34no—
46#65402—31no—
47#65399—31no—
48C24×C3×C5—21no—
49C2×C3×C5×Q8—21no—
50C2×C3×C5×Q8—22no—
51C2×C3×C5×Q8D414yescomplemented
52C2×C3×C5×Q8C2312yes—
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4—21no—
56C2×C3×C5×D4C2312yes—
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220—21no—
60C2×#1220—24no—
61C2×#1220D412yes—
62#6821—28no—
63#6821—24no—
64#6821—24no—
65Q8×D15—28no—
66Q8×D15—24no—
67Q8×D15—24no—
68#6817—216no—
69#6817—22no—
70#6817—22no—
71#6817—22no—
72#6817D414yescomplemented
73C2×D60—22no—
74C2×D60D411yescharacteristic
75C2×D60C2311yescharacteristic
76C2×C4×D15—22no—
77C2×C4×D15—21no—
78C2×C4×D15—22no—
79C2×C4×D15C2312yes—
80C2×Dic30—22no—
81C2×Dic30D411yescharacteristic
82C2×Dic30C2311yescharacteristic
83C3×C5×SD16—28no—
84C2×C3×C5×C8—22no—
85C2×C3×C5×C8C2312yes—
86#6719—21no—
87#6719—24no—
88#6716—24no—
89#6715—24no—
90C4⋊Dic15C2312yes—
91C4×Dic15—21no—
92#6710—22no—
93C2×C3⋊#168C2312yes—
94C2×#1007—51no—
95C22×C3×SD16D511yescharacteristic, complemented
96#5805—51no—
97C2×#932—51no—
98#5225—51no—
99#5172—54no—
100#5170—54no—
101#5113—51no—
102#5110—51no—
103C22×C5×Q8C2×D311yescharacteristic
104C22×C5×D4C2×D311yescharacteristic
105#4147—64no—
106#4147—64no—
107C2×#713—32no—
108C2×#713—61no—
109C2×Q8×D5—32no—
110C2×Q8×D5—61no—
111C2×#709—31no—
112C2×#709—31no—
113C2×#709—62no—
114C2×C5×SD16—24no—
115C2×C5×SD16C2×D314yes—
116C22×C5×C8C2×D311yescharacteristic
117#4099—62no—
118#4086—61no—
119#4084—34no—
120#4082—61no—
121C2×#687—32no—
122#4078—64no—
123C2×#686—32no—
124#4072—31no—
125C2×#681—31no—
126#3967—34no—
127#3953—32no—
128#3952—34no—
129#3948—32no—
130#3010—151noSylow
131C23×C3×C5—22no—
132C23×C3×C5—42no—
133C23×C3×C5—82no—
134C23×C3×C5C2×D411yescharacteristic
135C22×D15—21no—
136C22×D15C2×D412yes—
137C3×C5×Q8—24no—
138C3×C5×Q8—22no—
139C3×C5×Q8C2×D414yes—
140C3×C5×D4—22no—
141C3×C5×D4—22no—
142C3×C5×D4—42no—
143C2×C3×C4×C5—24no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5C2411yescharacteristic
149#1220—24no—
150#1220—24no—
151#1220—84no—
152C2×Dic15—21no—
153C2×Dic15—22no—
154C2×Dic15C2×D412yes—
155D60—28no—
156D60—22no—
157D60—21no—
158D60C2×D412yes—
159C4×D15—28no—
160C4×D15—28no—
161C4×D15—24no—
162C4×D15—22no—
163C4×D15—22no—
164Dic30—28no—
165Dic30—22no—
166Dic30—21no—
167Dic30C2×D412yes—
168C3×C5×C8—22no—
169C3⋊#168—22no—
170C22×C3×Q8C2×D511yescharacteristic
171C22×C3×D4C2×D511yescharacteristic
172#1007—104no—
173#1007—104no—
174C2×#239—52no—
175C2×#239—101no—
176C2×D3×Q8—52no—
177C2×D3×Q8—101no—
178C2×#235—51no—
179C2×#235—51no—
180C2×#235—102no—
181C2×C3×SD16—24no—
182C2×C3×SD16C2×D514yes—
183C22×C3×C8C2×D511yescharacteristic
184#953—102no—
185#940—101no—
186#938—54no—
187#936—101no—
188C2×#214—52no—
189#932—104no—
190C2×#213—52no—
191#926—51no—
192C2×#208—51no—
193#835—54no—
194#821—52no—
195(C2×D3)⋊C8—54no—
196#816—52no—
197C24×C5—21no—
198C2×C5×Q8—21no—
199C2×C5×Q8—22no—
200C2×C5×Q8#6714yescomplemented
201C2×C5×Q8C22×D312yes—
202C2×C5×D4—22no—
203C2×C5×D4—21no—
204C2×C5×D4—22no—
205C2×C5×D4C22×D312yes—
206C22×C4×C5—21no—
207C22×C4×C5C22×D311yescharacteristic
208C2×C22⋊D5—32no—
209C2×C22⋊D5—61no—
210C2×C22⋊D5—64no—
211#713—64no—
212#713—68no—
213#713—64no—
214Q8×D5—64no—
215Q8×D5—68no—
216Q8×D5—64no—
217#709—34no—
218#709—616no—
219#709—62no—
220#709—62no—
221#709—62no—
222C2×D20—31no—
223C2×D20—31no—
224C2×D20—62no—
225C2×C4×D5—32no—
226C2×C4×D5—62no—
227C2×C4×D5—62no—
228C2×C4×D5—61no—
229C2×Dic10—31no—
230C2×Dic10—31no—
231C2×Dic10—62no—
232C5×SD16—28no—
233C2×C5×C8—22no—
234C2×C5×C8C22×D312yes—
235C22⋊Dic5—64no—
236C22⋊Dic5—61no—
237#687—64no—
238#686—64no—
239C4⋊Dic5—32no—
240C4×Dic5—61no—
241#681—62no—
242C2×#168—32no—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—151no—
245C22×SD16D1511yescharacteristic, complemented
246#535—151no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—151no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5—42no—
254C22×C3×C5—44no—
255C22×C3×C5—84no—
256C22×C3×C5#12012yes—
257C22×C3×C5C22×D411yescharacteristic
258C2×D15—22no—
259C2×D15—22no—
260C2×D15—24no—
261C2×D15—42no—
262C3×C4×C5—24no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—22no—
267Dic15—22no—
268Dic15—42no—
269C24×C3—21no—
270C2×C3×Q8—21no—
271C2×C3×Q8—22no—
272C2×C3×Q8C22⋊D514yescomplemented
273C2×C3×Q8C22×D512yes—
274C2×C3×D4—22no—
275C2×C3×D4—21no—
276C2×C3×D4—22no—
277C2×C3×D4C22×D512yes—
278C22×C3×C4—21no—
279C22×C3×C4C22×D511yescharacteristic
280C2×#67—52no—
281C2×#67—101no—
282C2×#67—104no—
283#239—104no—
284#239—108no—
285#239—104no—
286D3×Q8—104no—
287D3×Q8—108no—
288D3×Q8—104no—
289#235—54no—
290#235—1016no—
291#235—102no—
292#235—102no—
293#235—102no—
294C2×D12—51no—
295C2×D12—51no—
296C2×D12—102no—
297C2×C4×D3—52no—
298C2×C4×D3—102no—
299C2×C4×D3—102no—
300C2×C4×D3—101no—
301C2×Dic6—51no—
302C2×Dic6—51no—
303C2×Dic6—102no—
304C3×SD16—28no—
305C2×C3×C8—22no—
306C2×C3×C8C22×D512yes—
307#217—104no—
308#217—101no—
309#214—104no—
310#213—104no—
311C4⋊Dic3—52no—
312C4×Dic3—101no—
313#208—102no—
314C2×C3⋊C8—52no—
315C23×C5—22no—
316C23×C5—42no—
317C23×C5—82no—
318C23×C5D3×D411yescharacteristic
319C22×D5—32no—
320C22×D5—61no—
321C5×Q8—24no—
322C5×Q8—22no—
323C5×Q8C2×#6714yes—
324C5×D4—22no—
325C5×D4—22no—
326C5×D4—42no—
327C2×C4×C5—24no—
328C2×C4×C5—22no—
329C2×C4×C5D3×D411yescharacteristic
330C2×C4×C5D3×D412yes—
331C2×C4×C5C2×#6712yes—
332C2×C4×C5C23×D311yescharacteristic
333C22⋊D5—64no—
334C22⋊D5—64no—
335C22⋊D5—244no—
336C2×Dic5—32no—
337C2×Dic5—61no—
338C2×Dic5—62no—
339D20—32no—
340D20—68no—
341D20—62no—
342D20—61no—
343C4×D5—68no—
344C4×D5—68no—
345C4×D5—64no—
346C4×D5—62no—
347C4×D5—62no—
348Dic10—32no—
349Dic10—68no—
350Dic10—62no—
351Dic10—61no—
352C5×C8—22no—
353#168—62no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—151no—
357C2×#41—152no—
358C2×#41—151no—
359C2×#41—302no—
360C2×#41—301no—
361C22×Q8—152no—
362C22×Q8—301no—
363C22×Q8C2×D1511yescharacteristic
364C22×D4C2×D1511yescharacteristic
365AGL(1,ℤ/8)—304no—
366C2×SD16—24no—
367C2×SD16—152no—
368C2×SD16C2×D1514yes—
369C2×D8—152no—
370C2×M16—151no—
371C22×C8C2×D1511yescharacteristic
372#127—301no—
373#124—301no—
374#121—154no—
375#120—302no—
376#117—151no—
377#103—154no—
378#103—152no—
379#102—152no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5—82no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385D15—42no—
386D15—42no—
387C23×C3—22no—
388C23×C3—42no—
389C23×C3—82no—
390C23×C3D4×D511yescharacteristic
391C22×D3—52no—
392C22×D3—101no—
393C3×Q8—22no—
394C3×Q8—24no—
395C3×Q8C2×C22⋊D514yes—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—42no—
399C2×C3×C4—22no—
400C2×C3×C4—24no—
401C2×C3×C4D4×D512yes—
402C2×C3×C4D4×D511yescharacteristic
403C2×C3×C4C2×C22⋊D512yes—
404C2×C3×C4C23×D511yescharacteristic
405#67—104no—
406#67—104no—
407#67—404no—
408C2×Dic3—52no—
409C2×Dic3—101no—
410C2×Dic3—102no—
411D12—52no—
412D12—108no—
413D12—101no—
414D12—102no—
415C4×D3—108no—
416C4×D3—108no—
417C4×D3—102no—
418C4×D3—102no—
419C4×D3—104no—
420Dic6—52no—
421Dic6—108no—
422Dic6—101no—
423Dic6—102no—
424C3×C8—22no—
425C3⋊C8—102no—
426C22×C5—22no—
427C22×C5—44no—
428C22×C5—42no—
429C22×C5—84no—
430C22×C5#93712yes—
431C22×C5C2×D3×D411yescharacteristic
432C2×D5—64no—
433C2×D5—62no—
434C2×D5—62no—
435C2×D5—122no—
436C4×C5—24no—
437C4×C5#93712yes—
438C4×C5C2×D3×D411yescharacteristic
439C4×C5C22×#6711yescharacteristic
440Dic5—62no—
441Dic5—62no—
442Dic5—122no—
443C24—21no—
444#41—154no—
445#41—3016no—
446#41—304no—
447#41—308no—
448#41—304no—
449#41—302no—
450#41—302no—
451#41—302no—
452C2×Q8—21no—
453C2×Q8—22no—
454C2×Q8—151no—
455C2×Q8—151no—
456C2×Q8—302no—
457C2×Q8—304no—
458C2×Q8—308no—
459C2×Q8—304no—
460C2×Q8#122014yescomplemented
461C2×Q8C22×D1512yes—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—22no—
465C2×D4—152no—
466C2×D4—151no—
467C2×D4—151no—
468C2×D4—302no—
469C2×D4—301no—
470C2×D4—304no—
471C2×D4C22×D1512yes—
472C22×C4—21no—
473C22×C4—152no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4—301no—
477C22×C4C22×D1511yescharacteristic
478SD16—28no—
479SD16—304no—
480D8—304no—
481M16—302no—
482C2×C8—22no—
483C2×C8—152no—
484C2×C8C22×D1512yes—
485C4⋊C4—152no—
486C22⋊C4—304no—
487C22⋊C4—301no—
488C42—301no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—44no—
492C22×C3—42no—
493C22×C3—84no—
494C22×C3#408312yes—
495C22×C3C2×D4×D511yescharacteristic
496C2×D3—104no—
497C2×D3—102no—
498C2×D3—102no—
499C2×D3—202no—
500C3×C4—24no—
501C3×C4#408312yes—
502C3×C4C2×D4×D511yescharacteristic
503C3×C4C22×C22⋊D511yescharacteristic
504Dic3—102no—
505Dic3—102no—
506Dic3—202no—
507C2×C5—22no—
508C2×C5—82no—
509C2×C5#576212yes—
510C2×C5C2×#93711yescharacteristic
511D5—122no—
512D5—122no—
513C23—22no—
514C23—42no—
515C23—82no—
516C23—152no—
517C23—301no—
518C23D4×D1511yescharacteristic
519Q8—24no—
520Q8—22no—
521Q8—152no—
522Q8—308no—
523Q8—302no—
524Q8—301no—
525Q8C2×#122014yes—
526D4—22no—
527D4—22no—
528D4—42no—
529D4—152no—
530D4—308no—
531D4—304no—
532D4—304no—
533D4—302no—
534D4—301no—
535D4—1204no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—152no—
539C2×C4—308no—
540C2×C4—308no—
541C2×C4—301no—
542C2×C4—304no—
543C2×C4—302no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4D4×D1511yescharacteristic
547C2×C4D4×D1512yes—
548C2×C4C2×#122012yes—
549C2×C4C23×D1511yescharacteristic
550C8—22no—
551C8—302no—
552C2×C3—22no—
553C2×C3—82no—
554C2×C3#6609612yes—
555C2×C3C2×#408311yescharacteristic
556D3—202no—
557D3—202no—
558C5#8386011yescharacteristic, complemented, Sylow
559C22—22no—
560C22—42no—
561C22—44no—
562C22—84no—
563C22—302no—
564C22—302no—
565C22—304no—
566C22—602no—
567C22#9182612yes—
568C22C2×D4×D1511yescharacteristic
569C4—24no—
570C4—302no—
571C4—302no—
572C4—602no—
573C4#9182612yes—
574C4C2×D4×D1511yescharacteristic
575C4C22×#122011yescharacteristic
576C3#1061559111yescharacteristic, complemented, Sylow
577C2—22no—
578C2—82no—
579C2—602no—
580C2—602no—
581C2#1175652112yes—
582C2C2×#9182611yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×SD16C2
socleC22×C3×C5C22×D4
hypercenterC22×SD16D15
hypocenterC3×C5#3010
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#92098C2semidirect
2. C22×C3×C5×SD16C2semidirect
3. #11756564C2semidirect
4. C2×#91821C2semidirect
5. #11751326C2semidirect
6. #11751273C2semidirect
7. #11751271C2semidirect
8. #11751214C2semidirect
9. #11751211C2semidirect
16. C2×#6821C22semidirect
18. C2×Q8×D15C22semidirect
34. #91119C22semidirect
35. #91105C22semidirect
36. #91104C22semidirect
37. #91100C22semidirect
40. C22×C5×SD16D3semidirect
51. C2×C3×C5×Q8D4semidirect
72. #6817D4semidirect
95. C22×C3×SD16D5semidirect
200. C2×C5×Q8#67semidirect
245. C22×SD16D15semidirect
272. C2×C3×Q8C22⋊D5semidirect
460. C2×Q8#1220semidirect
489. C3×C5#3010semidirect
558. C5#83860semidirect
576. C3#10615591semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#920982
C22×C3×C5×SD162
#117565642
C2×#918212
#117513262
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